Technical Field
The present disclosure relates to a z-axis MEMS (Micro-Electro-Mechanical System) detection structure.
Description of the Related Art
Z-axis inertial accelerometers of a MEMS type are known, which include microelectromechanical structures sensitive to accelerations acting in a direction orthogonal to a main plane of extension thereof and to the top surface of a corresponding substrate of semiconductor material (in addition possibly to being able to detect further accelerations acting in the same plane).
FIG. 1 and FIG. 2A show a MEMS structure of a known type, designated as a whole by reference number 1, belonging to a z-axis inertial accelerometer (which further comprises an electronic reading circuit, not illustrated, electrically coupled to the MEMS structure).
The MEMS structure 1 comprises a substrate 2 of semiconductor material, in particular silicon, having a top surface 2a, and an inertial mass 3, which is of conductive material, for example, appropriately doped epitaxial silicon, and is arranged above the substrate 2, suspended at a certain distance from its top surface 2a. 
The inertial mass 3 has a main extension in a horizontal plane xy, which is defined by a first axis x and a second axis y, which are orthogonal to one another, and is substantially parallel to the top surface 2a of the substrate 2 (in resting conditions, i.e., in the absence of accelerations or external stresses acting on the MEMS structure 1), and a substantially negligible dimension along an orthogonal axis z, which is perpendicular to the aforesaid horizontal plane xy (and to the aforesaid top surface 2a of the substrate 2) and forms with the first and second axes x, y a set of three Cartesian axes xyz.
The inertial mass 3 has a through opening, defining a window 4, which traverses it throughout its thickness, has in plane view a substantially rectangular shape extending in length along the second axis y, and is arranged at a certain distance from the centroid (or center of gravity) of the inertial mass 3. The window 4 consequently divides the inertial mass 3 into a first portion 3a and a second portion 3b, which are arranged on opposite sides with respect to the window itself along the first axis x, the first portion 3a having a dimension along the first axis x that is larger as compared the second portion 3b. 
The inertial mass 3 further has a plurality of holes 3′, of very small size as compared to the aforesaid window 4, which traverses it throughout its thickness, enabling, during manufacturing process, release of the inertial mass 3 (and consequent suspended arrangement over the substrate 2) by chemical etching of an underlying sacrificial material (in a way not illustrated herein).
The MEMS structure 1 further comprises a first detection electrode 5a and a second detection electrode 5b, which are of conductive material, for example, polysilicon, are arranged on the top surface 2a of the substrate 2, on opposite sides with respect to the window 4 along the first axis x, to be positioned respectively underneath the first and second portions 3a, 3b of the inertial mass 3. The first and second detection electrodes 5a, 5b have in top plane view, in a plane parallel to the horizontal plane xy, a substantially rectangular shape, elongated along the second axis y.
The first and second fixed electrodes 5a, 5b are directly anchored to the substrate 2 by respective anchorage regions 6a, 6b, which are, for example, of dielectric material and are arranged between the top surface 2a of the substrate 2 and the electrodes themselves. The anchorage regions 6a, 6b have substantially the same conformation (rectangular in top plane view) and dimensions as the respective detection electrodes 5a, 5b. 
The first and second fixed electrodes 5a, 5b define, together with the inertial mass 3, a first detection capacitor and a second detection capacitor with plane and parallel faces, the capacitances of which are designated by C1, C2, respectively, and have a given value of capacitance at rest (i.e., in the absence of displacement of the inertial mass 3).
The inertial mass 3 is anchored to the substrate 2 by a central anchorage element 7, constituted by a column or pillar element extending within the window 4, at the center thereof, starting from the top surface 2a of the substrate 2. The central anchorage element 7 is consequently equidistant from the fixed electrodes 5a, 5b along the first axis x, and corresponds to the single point of constraint of the inertial mass 3 to the substrate 2.
In particular, the inertial mass 3 is mechanically connected to the central anchorage element 7 by a first elastic anchorage element 8a and a second elastic anchorage element 8b, which are referred to hereinafter for simplicity as “springs” and extend within the window 4, aligned, with a substantially rectilinear extension, along an axis of rotation A parallel to the second axis y, on opposite sides with respect to the central anchorage element 7. Each spring 8a, 8b extends between the central anchorage element 7 and a side portion of the inertial mass 3 facing the window 4.
The springs 8a, 8b are designed to be compliant to torsion around their direction of extension, thus enabling rotation of the inertial mass 3 out of the horizontal plane xy, about the axis of rotation A defined by the same springs 8a, 8b. 
During operation, in the presence of an acceleration acting along the orthogonal axis z, the inertial mass 3 rotates, by inertial effect, around the axis of rotation A approaching one of the two detection electrodes 5a, 5b (for example, the first detection electrode 5a) and correspondingly moving away from the other of the two detection electrodes 5a, 5b (for example, from the second detection electrode 5b), thus generating opposed variations of the detection capacitances C1, C2.
The value of the detection capacitances C1, C2 depends, among other parameters, upon the size of the detection electrodes 5a, 5b (which are desired to have a sufficient extension in plane view), and the capacitive variation depends, among other parameters, upon the distance of the detection electrodes 5a, 5b from the axis of rotation A (the distance has to be, in fact, sufficient to cause an appreciable variation of the gap between the inertial mass 3 and the detection electrodes 5a, 5b).
A suitable reading electronics (not shown in FIG. 1) of the accelerometer, electrically coupled to the MEMS structure 1, receives at its input the capacitive variations of the detection capacitors C1, C2, and processes the same variations in a differential way (as a function of the difference C2-C1) for determining the value of acceleration acting along the orthogonal axis z.
The present Applicant has realized that the MEMS structure 1 described previously, albeit advantageously enabling detection of accelerations acting along the orthogonal axis z, may be subject to even relevant errors of measurement in the case where the substrate 2 undergoes deformation, for example, as the temperature varies or on account of mechanical stresses.
In a known way, the package of a microelectromechanical sensor is in fact subject to deformation as the temperature varies, which is due to the different coefficients of thermal expansion of the materials of which it is made, thus causing corresponding deformation of the substrate of the MEMS structure contained therein. Similar deformations may occur on account of particular stresses induced from outside, for example, when the package is soldered on a printed circuit, or due to absorption of humidity by the package constituent materials.
As shown schematically in FIG. 2a, in the presence of deformation of the substrate 2, the detection electrodes 5a, 5b, directly constrained thereto (these electrodes are in general formed on the top surface 2a of the same substrate 2) follow this deformation, whereas the inertial mass 3 is displaced by the inertial effect, tilting by a detection angle θr (measured with respect to the first axis x). Due to deformation, variations of the distances (or gaps) between the inertial mass 3 and the detection electrodes 5a, 5b thus arise and consequent variations of the detection capacitances C1, C2.
The present Applicant has thus realized that the deformation of the substrate 2 may cause a drift of the DC value, referred to “zero-g level” or “offset”, of the accelerations detected, directed along the orthogonal axis z.
In detail, reference may be made by way of example to FIGS. 2a and 2b (which are not drawn to scale; namely, the value of the angles is increased for purely illustrative purposes in FIG. 2b), which illustrate a generic cross-section of the z-axis detection structure along the axis x.
A deformation (which may be considered in the example a cubic deformation), of the substrate 2 and of the corresponding top surface 2a, causes inclination of the top surface of the detection electrodes 5a and 5b by deviation angles θs1 and θs2, respectively (it should be noted that each of these angles corresponds to the tangent to the curve of deformation of the substrate 2 at the center of each electrode for the cross-section along the first axis x considered).
It may happen that, on account of the deviation angles θs1 and θs2, differential capacitive variations of the detection capacitors C1, C2 that are not desired (in so far as they are not linked to the inertial effect) occur:ΔC1αθr−θs1 ΔC2αθr−θs2 
The resulting offset on the differential detection is thus given by the following expression:offset=ΔC2−ΔC1αθs1−θs2 and is variable as a function of the temperature, or in general of all those effects that are able to induce deformations of the substrate 2, and directly proportional to the difference between the deviation angles θs1 and θs2.